Among conventional devices of this type there is known a device composed of a female die, best seen in FIGS. 5 and 6 having an internal shape identical with the external shape of the tube upper part including the mouth portion, shoulder portion as well as a portion of the drum part of the tube to be formed and a punch 02 to be pressed into this female die. According to this method a ring-shaped aluminum material 03 element, after being loaded in the female die, is extended by pressing the punch 02 thereinto, thereby press-forming an aluminum tube. The load imposed on the female die and the punch at this press-forming time is very large; on this account, the part 01A of the female die corresponding to the drum part has hitherto been formed of a sintered hard alloy, and the other part 01B is made of quenched SKD-11 which is relatively low-priced and highly and serves as a disposable part. This not only makes the structure of the female die complex, but causes the price to rise. A factor in the large value of the load at the time of forming above-described is attributed to the flow of the aluminum. Thus as the punch 02 is pressed in, the aluminum is extruded to form the tube drum part, being pressed by the maximum diameter portion 02a under the shoulder portion of the punch 02. At this time, the aluminum placed above of the maximum diameter portion 02a receives an extraordinary compression and this pressure is exerted on the female die and the punch.